text:
\section{Introduction}\label{sec:01}

Spontaneous synchronization in populations of interacting units is a ubiquitous phenomena in complex systems~\cite{pikovsky2001syn,strogatz2003sync}. Describing such collective behaviors in terms of coupled phase oscillators and studying phase transitions between incoherence and synchrony have proven useful in of physics, biology and social systems~\cite{rohden2012self,montbrio2018kuramoto,ottino2018volcano}. Exploring the routes towards synchrony and uncovering the underlying mechanism in various levels have attracted increasing theoretical and experimental interests~\cite{kiss2002emerging,acebron2005the,skardal2015control}.

Most existing literatures focus on pairwise interaction between oscillators that typically contain the first harmonic based on a phase reduction~\cite{kuramoto1975,rodrigues2016the}. However, in many cases, one needs to go beyond such setups allowing for non-pairwise coupling that incorporates high order structures, i.e., simplexes~\cite{salnikov2019simplicial,gong2019low,bibk2016chaos,Ashwin2016PhysD,Leon2019PRE}, which have gained more attention in recent years. Recent advances demonstrate that the simplicial interactions, sometimes called hypernetworks, play essential roles in many systems ranging from signal transmission in neural networks to structural function correlation in brain dynamics~\cite{reimann2017cliques,billings2019simplex}. As shown in~\cite{tanaka2011multi,komarov2015finite,skardal2019abrupt}, notable features of higher-order interactions in coupled oscillator ensembles include the emergence of extensive multistability and a continuum of abrupt desynchronization transitions (ADTs), which lead to potential applications in memory and information storage. Despite these findings, a rigorous analysis of the bifurcations and stability properties that characterize both the macroscopic and microscopic dynamics is lacking, thereby leaving our understanding of these physical phenomena incomplete.

In this paper, we provide an analysis of synchronization transitions induced by simplicial interactions and nonlinear higher order coupling in oscillator ensembles. Using a self-consistent approach we perform a bifurcation analysis that uncovers a general phenomenon that gives rise to ADTs and extensive multistability. Furthermore, we establish scaling relations that describe the critical points for desynchronization that are universal in the sense that they do not depend on the functional form of the natural frequency distribution. Most importantly, we perform a rigorous stability analysis for finitely- and infinitely-many partially synchronized states with arbitrary system size using a spectral analysis of the stable cluster states. We reveal that a continuum of ADTs originate from the instability of a collective mode under the nontrivial antisymmetrical manifold in the high dimensional phase space.

The remainder of this paper is organized as follows. In Sec.~\ref{sec:02} we present a bifurcation analysis for the globally-coupled system. In Sec.~\ref{sec:03} we analyze the stability of cluster states and characterize the properties of the ADTs. In Sec.~\ref{sec:04} we briefly present an additional example of a system with frequency-weighted coupling. Finally, in Sec.~\ref{sec:05} we conclude with a discussion of our results.

\section{Bifurcation Analysis}\label{sec:02}

We consider oscillator ensembles with three-way nonlinear coupling whose evolution is given by
\begin{equation}\label{equ:01}
  \dot{\theta}_i=\omega_i+\frac{1}{N^2}\sum_{m=1}^{N}\sum_{n=1}^{N}K_{imn}\sin(\theta_m+\theta_n-2\theta_i),
\end{equation}
where $\theta_i$ is the phase of oscillator $i$ with $i=1,\ldots,N$, $N$ is the system size, and $\omega_i$ is the natural frequency of oscillator $i$, assumed to be drawn from a distribution $g(\omega)$, which is assumed to be even throughout this paper. Unlike the classical Kuramoto-like models, the coupling term in Eq.~(\ref{equ:01}) is not pairwise, but involves triplets. Finally, $K_{imn}$ is the coupling strength among triplet of oscillators $i$, $m$, and $n$. While we will consider more general cases below, we first restrict our attention to the simplest setup $K_{mni}=K\ge0$ (uniform coupling), in which case Eq.~(\ref{equ:01}) is equivalent to a fully connected hypernetwork topology~\cite{wang2010evolving}. (Later we will consider frequency-weighted coupling.)

Before proceeding with the bifurcation analysis, we introduce two order parameters to characterize the collective behavior of the ensemble, namely, $Z_k=R_k e^{i\Theta_k}=\frac{1}{N} \sum_{m=1}^\infty e^{ik\theta_m}$ for $k=1$ and $2$. In the case where a single synchronized cluster emerges the classical Kuramoto order parameter $Z_1$ is sufficient to describe the macroscopic synchronization dynamics. However, when two clusters emerge the Daido order parameter $Z_2$ measures the degree of (cluster) synchronization~\cite{daido1996multi}, while $Z_1$ measure the degree of asymmetry between the two clusters. $R_{k}$ and $\Theta_{k}$ correspond to amplitudes and arguments, respectively, of the order parameters. By exponentiating the sine term and distributing the summation, these definitions allow us to rewrite Eq.~(\ref{equ:01}) as
\begin{equation}\label{equ:02}
  \dot{\theta}_i=\omega_i+KR_1^2 \sin(2\Theta_1-2\theta_i),
\end{equation}
where $KR_1^2$ acts as an effective force on each oscillator aiming to entrain it via the mean field $\Theta_2$. The presence of a higher order harmonic ($\sim \sin2\theta_i$) and nonlinear coupling ($\sim KR_1^2$), gives rise to a series of nontrivial dynamical features.

Proceeding with our analysis, it is convenient to introduce the parameter $q=KR_1^2$.
Given the $SO_2$ group symmetry (i.e., rotation and reflection)~\cite{crawford1994amp} of Eq.~(\ref{equ:02}), we enter the appropriate rotating frame, i.e., consider the transformation $\theta\mapsto\theta+\Omega t$ (where $\Omega$ is the mean natural frequency), to obtain a non-rotating solution ($\dot{\Theta}_{k}=0$) and further set $\Theta_{k}=0$ by appropriately shifting initial conditions. In this case, the whole population can be divided into those phase locked oscillators ($|\omega_i|<q$) and that of drifting ones ($|\omega_i|>q$). For the phase locked case, the oscillators are entrained by the mean field, yielding fixed points $\dot{\theta}_i=0$ satisfying
\begin{align}
\sin 2\theta_i=\frac{\omega_i}{q}~~~\text{and}~~~\cos 2\theta_i=\sqrt{1-\frac{\omega_i^2}{q^2}}.\label{equ:02a}
\end{align}
In fact the second-order harmonic in yields two stable fixed points (as well as two unstable fixed points), which manifest in the formation of two clusters with phase difference $\pi$~\cite{dkardal2011cluster,komarov2013multi}. Trigonometric identities allow us to write
\begin{align}
\sin\theta_i=\frac{\sin 2\theta_i}{2\cos \theta_i}~~~\text{and}~~~\cos\theta_i=\pm\sqrt{\frac{1+\cos 2\theta_i}{2}},\label{equ:02b}
\end{align}
where the $+$ or $-$ in the cosine term determine whether $\theta_i$ falls in the cluster near $\theta=0$ or $\pi$, respectively. Here we replace the $\pm$ in the cosine term with the parameter $p_i$, which takes the value $1$ with probability $\eta(\omega_i)$ and is $-1$ with probability $1-\eta(\omega_i)$. Thus, $\eta(\omega_i)$ is an indicator function satisfying $0\leq\eta(\omega_i)\leq 1$ which represents the fraction of oscillators with natural frequency $\omega_i$ that become entrained to the $\theta=0$ cluster.

Turning briefly to the drifting oscillator population, each oscillator rotates non-uniformly on the unit circle with period $T_i=2\pi/\sqrt{\omega_i^2-q^2}$. Moreover, the contribution of drifiting oscillators to the order parameter $Z_k$ is given by $
\frac{1}{N}\sum_{|\omega_i|>q}\frac{1}{T_i}\int_{0}^{2\pi}\frac{e^{ik\theta_i}}{|\dot{\theta}_i|}d\theta_i$.  In fact, the symmetry of the natural frequency distribution causes this contribution to vanish, implying that drifting oscillators do not contribute to either order parameter $Z_{k}$ whether $N$ is finite or not. The contribution of the locked oscillators to the order parameters can be simplified by first noting that $Z_k=\frac{1}{N} \sum_{m=1}^\infty e^{ik\theta_m}=\frac{1}{N} \sum_{m=1}^\infty \cos(k\theta_m)+i\sin(k\theta_m)$. Similar to the drifting oscillators, the even and odd symmetries of the natural frequency distribution and sine term, respectively, cause the imaginary part to vanish, yielding $R_k=\frac{1}{N} \sum_{m=1}^\infty \cos(k\theta_m)$. Writing these  out explicitly, we have that
\begin{align}
R_1&=\frac{1}{N} \sum_{i=1}^\infty \cos(\theta_i)=\frac{1}{N} \sum_{i=1}^\infty p_i\sqrt{(1+\cos 2\theta_i)/2},\label{equ:03}\\
R_2&=\frac{1}{N} \sum_{i=1}^\infty \cos(2\theta_i)=\frac{1}{N} \sum_{i=1}^\infty \sqrt{1-(\omega_i/q)^2},\label{equ:04}
\end{align}
from which we see that $R_2$ is determined by the parameter $q=KR_1^2$ that controls the range of phase locking, whereas $R_1$ is further restricted by the indicator function $\eta$ that describes the distribution of $p_i$'s, reflecting the asymmetry of phase locked oscillators between two clusters, and therefore is of major importance. Converting sum in Eq.~(\ref{equ:03}) to a sum over frequencies (i.e., treating the population as a distribution) and replacing the cosine term, we find that the parameterized equation for determining $R_1$ is given by
\begin{equation}\label{equ:06}
  \frac{1}{\sqrt{K}}=\frac{1}{N}\sum_{|\omega_i|<q}[2\eta(\omega_i)-1]\sqrt{\frac{1+[1-(\omega_i/q)^2]^{\frac{1}{2}}}{2q}},
\end{equation}
where we denote the right hand side of Eq.~(\ref{equ:06}) as $F(q)$.

\begin{figure*}
  \centering
\footnotesize

  \includegraphics[width=0.55\linewidth]{fig1.eps}\\
  \caption{Bifurcation diagram of the order parameters $R_1$ (a), $R_2$ (b) with $K$ for the uniform coupling. The circles and solid lines represent the results obtained by numerical simulations and theoretical predictions (stable branches, $q>q_c$), respectively. $\eta=1$ (red), $0.95$ (green), $0.9$ (blue), $0.85$ (cyan), $0.8$ (pink) and $0.75$ (purple). Dashed line denotes the theoretical dependence between $R_1^c$ and $K_c$. For each value of $\eta$, the initial phases are set to $0$ and $\pi$ with probability $\eta$ and $1-\eta$, respectively, then $K$ decreases to $0$ and restores to initial value with $\Delta K=0.01$ adiabatically. In the simulation, $N=10^5$ and $g(\omega)=\frac{1}{2}$, $\omega\in (-1, 1)$.}\label{fig:01}
\end{figure*}

Importantly, Eq.~(\ref{equ:06}) implicitly links $R_{k}$, $K$, and $q$. The underlying bifurcations occur at a critical point $K_c$ given where $\frac{dR_{k}}{dK}|_{K=K_c}=\frac{dR_{k}}{dq}(\frac{dK}{dq})^{-1}|_{q=q_c}$ diverges. Since $F(q)$ is a continuous function we search for either the case $F'(q_c)=0$, which corresponds go a smooth fold bifurcation, or the case where $F'(q_c)$ does not exist, which corresponds to a non-smooth bifurcation. Consequently, the associated critical points are $K_c=F(q_c)^{-2}$ and $R_{k}^c=R_{k}(q_c)$.

To get analytical insights for the critical points, we consider a uniform constant indicator function $\eta(\omega_i)=\eta$. Then $F(q)$ can be simplified to $F(q)=(2\eta-1)f(q)$, where
\begin{align}
f(q)=\frac{1}{N}\sum_{|\omega_i|<q}\sqrt{\frac{1+[1-(\omega_i/q)^2]^{1/2}}{2q}}. \label{equ:06a}
\end{align}
For sufficiently small $K$ no solution exists except for $R_{k}=0$ (which always exists), but when $K$ is increased the bifurcation occurs at the critical value $K_c$ given by
\begin{equation}\label{equ:07}
  K_{c}(\eta)=[(2\eta-1) f(q_c)]^{-2},
\end{equation}
and the corresponding critical order parameters are
\begin{equation}\label{equ:08}
  R_1^c(\eta)=(2\eta-1)\sqrt{q_c}f(q_c),
\end{equation}
\begin{equation}\label{equ:09}
  R_2^c(\eta)=\frac{1}{N}\sum_{|\omega_i|<q_c}\sqrt{1-(\omega_i/q_c)^2}.
\end{equation}

Generically, $q_c$ and $f(q_c)$ are non-zero, indicating a discontinuous jump at $K_c$ between the synchronized (i.e., $R_{k}^c>0$) state and the incoherent (i.e., $R_{k}=0$). Moreover, the incoherent state remains stable for all $K$ in the $N\to\infty$ limit. These two criteria imply that the system undergoes, for a given value of $\eta,$ an ADT characterizing a discontinuous jump from a synchronized state to the incoherent state, but no complementary transition where the incoherent state spontaneously synchronizes. Moreover, a different ADT will occur at each different value of $\eta$, so in fact a continuum of ADTs exist. This phenomenon differs essentially from the traditional first-order phase transition characterized by a finite hysteresis loop~\cite{lee2009large,gomez2011exp} where (i) typically a single desynchronization transition occurs (often via a saddle-node bifurcation) and (ii) a complementary synchronization transition typically follows at a larger value coupling strength.

The self-consistent analysis and scaling formulas presented above capture the macroscopic dynamics exhibited by Eq.~(\ref{equ:01}) with arbitrary $g(\omega)$ and $N$. Note that both $K_c$ and $R_1^c$ exhibit a monotonic dependence on $\eta$ (decreasing and increasing, respectively), whereas $R_2^c$ remarkably remains constant. For instance, for the case of a standard normal frequency distribution, i.e., $g(\omega)=\frac{1}{\sqrt{2\pi}}e^{-\frac{\omega^2}{2}}$~\cite{komarov2015finite}, the ADTs occur at $q_c=1.456$, $f(q_c)=0.679$. For the case of a Lorentzian distribution with unit width, i.e., $g(\omega)=\frac{1}{\pi (\omega^2+1)}$~\cite{skardal2019abrupt}, we have critical points $q_c=1.463$, $f(q_c)=0.491$. Note that for both cases the function $f(q)$ is smooth. However, for the non-smooth and finitely-supported uniform distribution $g(\omega)=\frac{1}{2}$ for $\omega\in (-1,\, 1)$, we have critical points at $q_c=1$ since
\begin{align}
f(q)=\left\{\begin{array}{rl}\frac{2\sqrt{2q}}{3}&\text{if }q<1,\\ \frac{\sqrt{2}\sqrt{q+(q^2-1)^{\frac{1}{2}}}(1+q^2-q\sqrt{q^2-1})}{3q}&\text{if }q\geq1.\end{array}\right.
\end{align}
Moreover, $f'(q_c)$ does not exist since $f'(q_c^+)\neq f'(q_c^-)$, then the corresponding critical points are $K_c=\frac{9}{8(2\eta-1)^2}$ with
\begin{align}
R_1^c=\frac{2\sqrt{2}}{3}(2\eta-1)=\frac{1}{\sqrt{K_c}},~~~\text{and}~~~R_2^c=\frac{\pi}{4}.\label{equ:09a}
\end{align}
In Fig.~(\ref{fig:01}) we illustrate our results for the uniform distribution, plotting the order parameters $R_1$ and $R_2$ in panels (a) and (b), respectively, using $\eta=1$ (red), $0.95$ (green), $0.9$ (blue), $0.85$ (cyan), $0.8$ (pink), and $0.75$ (purple). Analytical predictions are plotted as solid curves, while results from simulations with $N=10^5$ oscillators are plotted with circles, both as the coupling strength is decreased from a synchronized cluster state and increased from the incoherent state. the analytical prediction matches simulations. Critical values $R_1^c$ and $R_2^c$ are plotted as dotted curves, indicating the continuum of ADTs. Analytical predictions match the simulation results very well.

\section{Stability}\label{sec:03}

To better understand the system dynamics, we consider the structural stability question of what cluster states emerge from an arbitrary configuration. A linear stability analysis demonstrates that the incoherent state can never lose its stability for any $K$. This follows from the fact that the continuous spectrum of the incoherent state, i.e., $R_{k}=0$, is purely imaginary ($i\omega$) and the nonlinear mean field has no contribution to discrete spectrum~\cite{strogatz1991stability}. Thus due to the purely nonlinear interaction term in Eq.~(\ref{equ:02}) it is impossible for a spontaneous phase transition from the incoherent state. We therefore aim to investigate the stability of partially synchronized states, first focusing on finite $N$ case, which then turns out to generalize to the thermodynamic limit $N\to\infty$ directly.

\begin{figure*}
  \centering

  \includegraphics[width=0.55\linewidth]{fig2.eps}\\
  \caption{Bifurcation diagram of the order parameters $R_1$ (a), $R_2$ (b) with $K$ for the frequency weighted coupling, $g(\omega)=\frac{1}{\pi(\omega^2+1)}$. Circles are numerical simulations and solid lines are theoretical results (stable branches, $q>q_c$). $\eta=1$ (red), $0.95$ (green), $0.9$ (blue), $0.85$ (cyan), $0.8$ (pink) and $0.75$ (purple). (c) Analytical relation between $R_1^c$ and $K_c$ (black solid line) with $g(\omega)=\frac{1}{\sqrt{2\pi}}e^{-\frac{\omega^2}{2}}$, blue circles represent numerical simulations with different $\eta$, which is in agreement with the dashed line (a) representing universal phase transition. (d) Sketch map of the stable configuration, the blue arrows (red) stand for a/an stable (unstable) perturbed direction. Numerical strategy is the same as Fig.~(\ref{fig:01}).}\label{fig:02}
\end{figure*}

The $SO_2$ group symmetry ensures that the drifting oscillators generate a purely imaginary spectrum in the linear stability analysis, thereby having no contributions to the mean field~\cite{omel2012non,omel2013bifurcation}. In other words, they effectively decouple from the locked oscillators in Eq.~(\ref{equ:02}), so we can only consider $N_l$ oscillators locked to the mean field for some $q$ excluding the drifting ones. We note, however, that in some cases, such as uniformly-distributed frequencies, all oscillators become locked in a synchronized state, yielding $N_l=N$~\cite{mirollo2005spe}. To study stability of such partially synchronized states, we consider a small perturbation $x_i$, $|x_i|\ll1$, on each phase locked oscillator $\theta_i$ in Eq.~(\ref{equ:02}) and, after neglecting high order terms, the evolution for perturbation satisfies $\dot{\mathbf{x}}=\mathbf{J}\mathbf{x}$ where $\mathbf{x}=(x_1,\ldots, x_{N_l})$ and $\mathbf{J}$ is the Jacobian matrix with entries $J_{ij}=\frac{\partial \dot{\theta}_i}{\partial \theta_j}$. In fact, $\mathbf{J}$ is of the form
\begin{equation}\label{equ:13}
  \mathbf{J}=\frac{2KR_1}{N}\mathbf{M}-2q\mathbf{D},
\end{equation}
where the matrix $\mathbf{M}$ is given by $M_{ij}=\cos(\theta_j-2\theta_i)$ and a diagonal matrix $\mathbf{D}$ is given by $D_{ij}=\cos(2\theta_i)\delta_{ij}$. The stability properties for a given cluster state is then determined by the eigenvalues of $\mathbf{J}$. First, note that $\sum_{j=1}^{N_l} J_{ij}=0$, which gives a trivial eigenvalue $\lambda=0$ (with constant eigenvector $\mathbf{v}\propto\mathbf{1}=(1,\ldots,1)$) that corresponds to the rotation invariance of Eqs.~(\ref{equ:01}) and (\ref{equ:02}). The remaining $N_l-1$ eigenvalues can be calculated via the characteristic equation of $\mathbf{J}$, which can be expressed as $B(\lambda)=\text{det}(\lambda\mathbf{I}-\mathbf{J})$. Next, by defining
\begin{align}
\mathbf{E}=\frac{\lambda \mathbf{I}}{2K R_1}+R_1\mathbf{D},
\end{align}
one may write
\begin{align}
2KR_1\mathbf{E}(\mathbf{I}-\mathbf{E}^{-1}\mathbf{M}/N).
\end{align}
Thus, the characteristic polynomial takes the form
\begin{align}
B(\lambda)=2KR_1 \text{det}(\mathbf{E})\text{det}(\mathbf{I}-\frac{1}{N}\mathbf{E}^{-1}\mathbf{M}).
\end{align}
Finally, assuming that $\mathbf{E}$ must is in fact invertible, we have that $det(\mathbf{E})\neq 0$, and the key task for calculating the eigenvalue spectrum depends on finding the roots of the last term alone.

Next we ease notation by defining four vectors $\mathbf{c}^{(k)}$ with $c_i^{(k)}=\cos k\theta_i$ and $\mathbf{s}^{(k)}$ with $s_{i}^{(k)}=\sin k\theta_i$ that satisfy the orthogonality property $\mathbf{c}^{(k)}\cdot \mathbf{s}^{(k')}=0$ ($k'=1,2$). We note here that $k=2$ corresponds to purely deterministic vectors, while $k=1$ is random vectors due to clustering and multi-branches. That is, the entries of $\mathbf{c}^{(2)}$ and $\mathbf{s}^{(2)}$ do not depend on whether a given oscillator falls in the $0$ or $\pi$ cluster, but the entries of $\mathbf{c}^{(1)}$ and $\mathbf{s}^{(1)}$ do. Moreover, we note that the rank of $\mathbf{M}$ is only $2$ since, for all $\mathbf{x}\in \mathbb{R}^{N_l}$, we have $\mathbf{M}\mathbf{x}=(\mathbf{c}^{(1)}\cdot\mathbf{x})\mathbf{c}^{(2)}+(\mathbf{s}^{(1)}\cdot\mathbf{x})\mathbf{s}^{(2)}$. Introducing the orthonormal basis $\mathbf{a}_1=\frac{\mathbf{c}^{(1)}}{\|\mathbf{c}^{(1)}\|}$ and $\mathbf{a}_2=\frac{\mathbf{s}^{(1)}}{\|\mathbf{s}^{(1)}\|}$, the matrix $\mathbf{E}^{-1}\mathbf{M}/N$ restricted to the subspace that is spanned by $\{\mathbf{a}_{i}\}$ turns out to be a $2\times 2$ matrix $\mathbf{Q}$, i.e., $(\mathbf{E}^{-1}\mathbf{M}/N)_{\mathbf{a}_1,\mathbf{a}_2}=\mathbf{Q}(\lambda)$.
The entries of this matrix are defined as $Q_{ij}=\mathbf{a}_i\cdot\frac{1}{N}\mathbf{E}^{-1}\mathbf{M}\mathbf{a}_j$, whose diagonal entries are
\begin{equation}\label{equ:17}
  Q_{11}=\frac{1}{N}\sum_{i=1}^{N_l} [2\eta(\omega_i)-1]\frac{2KR_1 |c_i^{(1)}| c_i^{(2)}}{\lambda+2qc_i^{(2)}},
\end{equation}
\begin{equation}\label{equ:20}
  Q_{22}=\frac{1}{N}\sum_{i=1}^{N_l} [2\eta(\omega_i)-1]\frac{KR_1 (s_i^{(2)})^2/ |c_i^{(1)}|}{\lambda+2qc_i^{(2)}},
\end{equation}
and the off-diagonal $Q_{ij}\propto \frac{1}{N}\sum_{m=1}^{N_l} \frac{c_m^{(i)}s_m^{(j)}}{E_{mm}}$ with $i\neq j$, while the other $N_l-2$ basis vectors span the kernel of $\mathbf{E}^{-1}\mathbf{M}/N$. Orthogonality implies that $Q_{12}$ and $Q_{21}$ are zero, so the characteristic polynomial simplifies to
\begin{equation}\label{equ:21}
  B(\lambda)=2KR_1 \prod_{i=1}^{N_l} E_{ii}[1-Q_{11}(\lambda)][1-Q_{22}(\lambda)].
\end{equation}

In fact, the rational functions $Q_{jj}(\lambda)$ ($j=1, 2$) are strictly decreasing away from their $\frac{N_l}{2}$ poles $\lambda_i=-2qc_i^{(2)}$ ($\lim_{\lambda\to \lambda_i^\pm}Q_{jj}(\lambda)=\pm\infty$), so $Q_{jj}(\lambda)=1$ must have one route between two consecutive poles. The necessary condition for stable locked state requires all $c_i^{(2)}>0$. In addition, we find that $Q_{11}(0)=1$ corresponds to a trivial eigenvalue $\lambda=0$. The remaining one eigenvalue is uniquely determined by $Q_{22}(\lambda)=1$ for $\lambda>\lambda_i$. Since $Q_{22}(\lambda)$ is decreasing, the root is negative if and only if $Q_{22}(0)<1$, which leads to the structural stability condition for the configuration of population
\begin{equation}\label{equ:22}
  \frac{1}{N}\sum_{i=1}^{N_l} [2\eta(\omega_i)-1]\frac{KR_1 (s_i^{(2)})^2}{2q|c_i^{(1)}|c_i^{(2)}}<1,
\end{equation}
or equivalently, $F'(q)<0$. Therefore, we conclude that the eigen-spectrum of $\mathbf{J}$ is made up of three parts, a heavily populated part consisting of $N_l-2$ negative eigenvalues within the poles, a trivial part $\lambda=0$ corresponding to rotation invariance, and a lone eigenvalue outside the poles. In the thermodynamic limit $N\to\infty$, the first part merges into continuous spectrum with $\lambda(\omega)=-2\sqrt{q^2-\omega^2}$, while the last part turns out to be a nontrivial discrete spectrum determined by the continuum limit $Q_{22}(\lambda)=1$ ($\lambda \neq \lambda(\omega))$.

It is also instructive to characterize the eigenvectors of $\mathbf{J}$. Considering a frequency-dependent vector $\mathbf{x}\in\mathbb{R}^{N_l}$ with $x_i=\chi(\omega_i)$, the space $\mathbb{R}^{N_l}$ can be split into two subspaces $V_{even}$ and $V_{odd}$. If $\chi$ is an even (or odd) function, then $\mathbf{x}\in V_{even}$ (or $V_{odd}$). This definition allows $\mathbf{x}$ to be random vector, such as $\mathbf{c}^{(k)}\in V_{even}$, $\mathbf{s}^{(k)}\in V_{odd}$, so $V_{even}\perp V_{odd}$ and $V=V_{even}\oplus V_{odd}$. The eigenspace of $\mathbf{J}$ can be described via the basis of $V_{even}$ and $V_{odd}$. For $\mathbf{x}^e\in V_{even}$, we have $\mathbf{J}\mathbf{x}^e=\frac{2KR_1}{N}\mathbf{c}^{(2)}(\mathbf{c}^{(1)}\cdot\mathbf{x}^e)-2q\mathbf{D}\mathbf{x}^e$. Setting $\mathbf{c}^{(1)}\cdot \mathbf{x}^e=1$, the eigenvector equation $\mathbf{J}\mathbf{x}^e=\lambda\mathbf{x}^e$ implies that $x_i^e=c_i^{(2)}/[NE_{ii}(\lambda)]$ in which $\lambda$ is a root of $Q_{11}(\lambda)=1$. Similarly, if $\mathbf{x}^o\in V_{odd}$, imposing $\mathbf{s}^{(1)}\cdot\mathbf{x}^o=1$, we obtain $x_i^o=s_i^{(2)}/[NE_{ii}(\lambda)]$ corresponding to $Q_{22}(\lambda)=1$. It is worth mentioning that $\mathrm{Re}[\nabla (Z_k)\cdot \mathbf{x}^{e}]=0$ and $\mathrm{Im}[\nabla(Z_k)\cdot\mathbf{x}^o]= 0$.

The structural stability of the clusters can then be interpreted as follows. Recall that, after entering a rotating frame and shifting initial conditions we have the mean phases $\Theta_{k}=0$. This corresponds to two clusters: one centered at $\theta=0$ and the other at $\theta=\pi$. Preserving this particular symmetry, perturbation may then contract or spread oscillators in each cluster, effectively pulling oscillators along the unit circle in the real or imaginary directions, respectively. Our analysis above reveals that the eigenvalues determined by $Q_{11}(\lambda)=1$ correspond to even eigenvectors, i.e., symmetric perturbation, that induce purely imaginary displacement of the centroid of configuration in the linear approximation, thereby inducing a small spread in each cluster. On the other hand, the eigenvalues for $Q_{22}(\lambda)=1$ correspond to odd eigenvectors, i.e., antisymmetric perturbation, that leads to purely real displacement of the centroid, thereby contracting each cluster. As the structure parameter $q$ is decreasing, the nontrivial solitary eigenvalue is shifted towards positive real axis and collides with the origin at $q=q_c$. Thus, the continuum of ADTs originate from the instability of a collective mode under the nontrivial antisymmetric perturbation in the high dimensional phase space associated with this solitary eigenvalue.

\section{Another Example: Frequency-Weighted Coupling}\label{sec:04}

Lastly, we show that our theory generalizes by considering the coupling heterogeneity of the form $K_{mni}=K|\omega_i|$, i.e., establishing the correlation between oscillators frequency and coupling strength as in Refs.~\cite{zhang2013exp,bi2016coe} that generates explosive synchronization and quantized time-dependent clustering. We show that such a frequency-weighted coupling scheme captures the essential properties of simplicial dynamics and can achieve certain cluster arrangement. In this case, the $SO_2$ group symmetry still holds, and the mean-field equation can be written as
\begin{align}
\dot{\theta}_i=\omega_i-q|\omega_i|\sin(2\theta_i).
\end{align}
If $q<1$, no oscillators are entrained by the mean-field indicating the asynchronous state. Interestingly, once $q\geq 1$, all oscillators become phase-locked ($N_l=N$) with $c_i^{(2)f}=\sqrt{1-q^{-2}}$ and $s_i^{(2)f}=\omega_i/(q|\omega_i|)$. The parametric function $F(q)$ is a smooth function for a constant $\eta$, i.e.,
\begin{align}
F(q)=(2\eta-1)\sqrt{[1+(1-q^{-2})^{\frac{1}{2}}]/(2q)},
\end{align}
and the fold bifurcation characterizing a continuum of universal ADTs occurs at $q_c=2/\sqrt{3}$ with
\begin{align}
K_c=\frac{8}{3\sqrt{3}(2\eta-1)^2},~~R_1^c=\frac{\sqrt{3}(2\eta-1)}{2},~~\text{and}~~R_2^c=\frac{1}{2}.
\end{align}
The results are presented in Fig.~\ref{fig:02} (a)--(c) (details similar to those for Fig.~\ref{fig:01}), displaying remarkable agreement between theory and simulation.

The stability analysis for the multi-clusters follows the similar way, where the Jacobian matrix is
\begin{align}
\mathbf{J}^f=\mathbf{W}(\frac{2KR_1}{N}\mathbf{M}-2q\mathbf{D})
\end{align}
with the frequency matrix $\mathbf{W}$ being $W_{ij}=|\omega_i|\delta_{ij}$. The resulting characteristic polynomial is
\begin{align}
B^f(\lambda)=2KR_1 \text{det}(\mathbf{E}^f)[1-Q_{11}^f(\lambda)][1-Q_{22}^f(\lambda)],
\end{align}
where
\begin{align}
\mathbf{E}^f&=\frac{\mathbf{W}^{-1}\lambda\mathbf{I}}{2KR_1}+R_1\mathbf{D},\\
Q_{11}^f&=\frac{1}{N}\sum_{i=1}^{N}\frac{c_i^{(1)f} c_i^{(2)f}}{E_{ii}^f(\lambda)},~~\text{and}\\
Q_{22}^f&=\frac{1}{N}\sum_{i=1}^{N}\frac{s_i^{(1)f} s_i^{(2)f}}{E_{ii}^f(\lambda)}.
\end{align}
The eigenvalue spectrum together with the associated eigenvectors has the same appearance as uniform coupling. In particular, the phase locked states exhibit fixed cluster arrangement regardless of $g(\omega)$, namely, the oscillators are recruited into two symmetric groups $\pm\theta^*$ ($\eta=1$) or four groups $\pm\theta^*$, $\pi\pm\theta^*$ ($\eta<1$). These different clusters can be understood as distinct picks in the information storage, while the stable configuration for the multi-clusters $Q_{22}^f(0)<1$ is equivalent to $\tan\theta^*\cdot \tan 2\theta^*<1$ impling $\theta^*<\frac{\pi}{6}$. Decreasing $q$ makes the symmetric clusters move away from each other (Fig.~(\ref{fig:02})d) and the configuration becomes unstable once $q<q_c$. The ADTs occur owing to a saddle node bifurcation where all oscillators become unlocked corresponding to the resting state.

\section{Discussion}\label{sec:05}

Summarizing, we have presented rigorous analytical descriptions for the collective dynamics in a population of globally coupled phase oscillators with higher-order interactions via simplicial structure. Extensive multistability of clusters and ADTs emerge directly from these higher order interactions and the nonlinear mean field. These results were obtained using a self-consistency analysis and rigorous bifurcation theory and reveal scaling properties of the transitions in the form of dependence of the critical points on the indicator and structural constants. The rigorous characterization of the eigenvalue spectrum presented above demonstrates that the stability properties of infinite many partially synchronized states are controlled by a nontrivial solitary eigenvalue, while the occurrences of ADTs correspond to the instability of a collective mode

\section*{ACKNOWLEDGEMENTS}

C. X. and X. W. acknowledge support from the National Natural Science Foundation of China (Grants Nos. 11905068 and 11847013).

redpajama_set_name: RedPajamaArXiv


Southern California's Halloween haunt event, Knott's Scary Farm, returns for its 45th season with 13 themed mazes and the return of Elvira, Mistress of the Dark for her last performance at Scary Farm with an all-new show.
Pumpkin Eater – Guests must attempt to survive the clutches of a 7-foot-tall creature that haunted the woods surrounding The Hollow. This fearsome creature is on the prowl, hidden in the shadows of the haunted town. To escape, each guest must go on their quest through the silent town filled with victims, through a cave of insects and through a thorny labyrinth that blocks the way out.
Trick-or-Treat: Lights Out – The classic maze returns with more scares than ever before, as guests step into the Green Witch's home and travel its dark walkways in this maze, armed with only a flashlight. Guests will face this maze completely in the dark, unaware of the new state-of-the-art effects and unexpected scares that await them.
Dark Ride – Guests will traverse through an abandoned carnival ride, which has become a safe haven for sideshow freaks who have turned this former attraction into a place of sheer terror.
Shadow Lands – Guests must face demon samurais whose souls are cursed for eternity to purgatory in this maze, as they embark on a quest through a shrine, an ancient Japanese temple and straight into the shadow lands.
Red Barn – The blood-drenched Red Barn has re-opened its doors, allowing the bloodthirsty animals inside to venture out for human flesh in the park's goriest maze. The legend of the Red Barn tells that the farmer who owns it was turned into a terrifying creature, and would send his sons to search for food and new victims.
PARANORMAL, INC. – This maze returns to Hayden Hill for another year of thrills and chills. Featuring aerial stunts and scares, guests will enter a haunted hospital full of demonic spirits.
The Tooth Fairy – The tooth fairy steals more than teeth, dragging his victims out of windows and into a world of teeth-chattering horror. This maze includes a blackout room where guests must feel their way out, an x-ray strobe light room, and an encounter with the tooth fairy himself.
Special Ops: Infected – Armed with laser guns, guests will have to defend the city against the zombie horde and find the cure for the infection. This maze includes ravenous zombies, more targets than ever, and plenty of surprises.
Voodoo – Order of the Serpent – The legend of Papa Legba continues as he leads guests through a journey to bring about the serpent demon goddess in New Orleans. Guests will venture through the swamps of the Deep South, filled with creatures looking for their next sacrifice, and demons looking to curse their victims with voodoo hexes.
The Hanging – A live stage show on the Calico Mine stage that looks back at the pop culture hits and misses of the year with plenty of laughs in store.
Knott's Scary Farm will have more than just mazes, thanks to the four scare zones that make sure guests have nowhere to hide.
Ghost Town Streets, the original and largest zone, will be filled with half-human, half-animal monsters that prowl the streets. Fiesta De Los Muertos will feature colorful costumes and stilt walkers. CarnEVIL rules the streets in the Boardwalk, filled with terrifying clowns. For the second year, The Hollow scare zone returns as guests find themselves among three covens of witches and their legions of the undead.
Guests can enjoy Knott's Scary Farm through single night tickets for $35 online and $75 at the gate; and the Knott's Scary Farm Pass, which offers unlimited visits to all 25 night events at $80 for Season Passholders and $90 for non-passholders.
For more information on Knott's Scary Farm, and to purchase tickets, visit KnottsScaryFarm.com.


New Delhi: Reliance Industries and British energy giant BP Plc will acquire their cash-strapped partner Niko Resources' 10% stake in gas discovery block NEC - 25 in the Bay of Bengal.
In mid-2015, Niko had chosen to withdraw from the NEC-25 block and relinquish its interest to the remaining stakeholders. RIL is the operator of the block with 60% interest while BP of the UK has the remaining 30 per cent stake.
"The application for assignment of Niko's PI (participating interest) to BP and RIL has been submitted and the same is awaiting Government of India approval," RIL stated in its notes to 2016-17 earnings last week. Niko's 10 per cent interest will be split between RIL and BP in proportion to their equity stake.
Gas discoveries in North-East Coast block NEC-0SN-97/1 (NEC-25) hold recoverable reserves of 1.032 trillion cubic feet.
The Canadian company has been facing cash problems and had even put up for sale its interest in NEC-25 as well as 10% stake in RIL's Krishna Godavari basin oil and gas producing block KG-DWN-98/3 or KG-D6. It has not been able to find a buyer though.


Frank Burton & Sons Fine Kitchens & Bathrooms by Skilled Craftsmen.
Welcome to Frank Burton & Sons; Home of Custom Kitchens & Bathrooms by Skilled Craftsmen.
We have a large stock of custom showers, tubs, and toilets, along with many quality fixtures and accessories.
We carry a full line of plumbing parts. Pipes, valves, faucets and much more!
We also carry a full line of hardware; screws to glues too. Why not shop local?
Signup to receive our monthly email blast filled with Special Offers, Practical Tips and More!
Sign Up for Burton's E-mail Blasts?


text:
Freshman Casey Burge, who picked up his third win of the year in four decisions, said a key was hitting the ball early.
"We need to play good defense and score early," he said. "Playing defense, throwing strikes, and hitting early is the only way to win a ballgame."
East Central coach Bo Long believed the game continued a four-game trend as the Hornets bats went cold.
"We are not swinging the bat that well right now, and it's a bad time to go into a slump," Long said. "Maybe we will break out of it tomorrow. Somebody has got to make the big hit."
The first six Tornado hitters reached base in the first, three on hits, as Purvis scored its only runs of the game early. East Central pitcher Dylan Hall struggled in the first, walking Brady Farlow and hitting Blaine Vowell with the bases loaded to force two runs across the plate. However, Hall was able to get out of the inning when Burge grounded out to Hornets shortstop Reis Trager to start a double play.
"Getting up early in the game helped me a lot," Burge said. "It was fun."
Burge made the two runs stick for Purvis (12-9), getting the first eight Hornet batters out. Josh Avila walked in the third to break up the early perfect-game attempt.
In the fourth inning, Burge started to tire. Will Garriga led off with a single for East Central (11-10). A Burge throwing error on Jacob Vick's bunt, followed by a wild pitch, left runners on second and third for the Hornets with one out. After the wild pitch, Burge intentionally walked Brad Cumbest to load the bases.
Burge got the second out on a strikeout before walking Louis Morgan for East Central's only run. He then induced a grounder back to the mound to leave the bases loaded and get out of the inning.
The Hornets had a chance to pull even in the fifth inning on back-to-back two-out singles from Garriga and Vick. However, Burge would strand the two East Central runners, getting the third out on a fly ball to right.
Ian Vowell finished the game for Burge to collect his first save of the year. Vowell allowed a swinging bunt two-out single to Morgan in the sixth inning and a two-out seventh-inning double to Garriga. Vowell got out of the sixth with a strike out and ended the game on a fly ball to third.
"I was getting tired," Burge admitted. "I felt good about the game. I knew that (Vowell) would go out and shut them down."
Hall started slowly, but recovered quickly. Starting with the double play to end the first inning, Hall 10 consecutive Purvis batters before Myles Kendrick started the Tornado fifth with a single. With one out, Logan Lambeth walked and Vowell followed with a single to load the bases.
However, Purvis would not add any more runs in the inning as Hall induced a bouncer to third. Hornets third baseman Trenton Baldock won the race to third and then threw across the diamond to first for East Central's second defensive inning-killing, bases-loaded double play.
"Hall settled down after a rough first inning," Long said. "After the first inning, he pitched a great game. He only gave up two runs."
Burge pitched the first five innings for the win, giving up three hits and three walks, including an intentional walk. He struck out two batters and the run he gave up was unearned.
Vowell had two singles to lead Purvis at the plate. Lambeth, a single and walk, and Kendrick, a single and hits batsman, reached base twice for the Tornadoes.
Hall would pitch into the seventh for East Central, getting the first out on a pop to the mound and hitting Kendrick before giving way to Blake Duvall, who got the final two outs for the Hornets.Hall took the hard-luck loss, giving up five hits - only two after the first inning - walking three batters and hitting two batters. He struck out three batters.
Garriga went 3-for-4 with a double and stolen base to get three of the Hornets' five hits.

redpajama_set_name: RedPajamaCommonCrawl


Unlike the other squares, the early Southwest Square was never used as a burial ground, although it offered pasturage for local livestock and a convenient dumping spot for "night soil". History By the late 1700s the square was surrounded by brickyards as the area´s clay terrain was better suited for kilns than crops. In 1825 the square was renamed in honor of Philadelphian David Rittenhouse, the brilliant astronomer, instrument maker and patriotic leader of the Revolutionary era. A building boom began by the 1850s, and in the second half of the 19th century the Rittenhouse Square neighborhood became the most fashionable residential section of the city, the home of Philadelphia´s "Victorian aristocracy." Some mansions from that period still survive on the streets facing the square, although most of the grand homes gave way to apartment buildings after 1913. In 1816, local residents loaned funds to the city to buy a fence to enclose Rittenhouse Square. In the decade before the Civil War, the Square boasted not only trees and walkways, but also fountains donated by local benefactors – prematurely, it turned out, for the fountains created so much mud that City Council ordered them removed. The square´s present layout dates from 1913, when the newly formed Rittenhouse Square Improvement Association helped fund a redesign by Paul Philippe Cret, a French-born architect who contributed to the design of the Benjamin Franklin Parkway and the Rodin Museum. Although some changes have been made since then, the square still reflects Cret´s original plan. Layout The main walkways are diagonal, beginning at the corners and meeting at a central oval. The plaza, which contains a large planter bed and a reflecting pool, is surrounded by a balustrade and ringed by a circular walk. Classical urns, many bearing relief figures of ancient Greeks, rest on pedestals at the entrances and elsewhere throughout the square. Ornamental lampposts contribute to an air of old-fashioned gentility. A low fence surrounds the square, and balustrades adorn the corner entrances. Oaks, maples, locusts, plane trees, and others stand within and around the enclosure, and the flowerbeds and blooming shrubs add a splash of color in season. Rittenhouse Square is the site of annual flower markets and outdoor art exhibitions. More than any of the other squares, it also functions as a neighborhood park. Office workers eat their lunches on the benches; parents bring children to play; and many people stroll through to admire the plants, sculptures, or the fat and saucy squirrels. Public Art Like Logan Square, you can see several of the city´s best-loved outdoor sculptures in Rittenhouse Square. The dramatic Lion Crushing a Serpent by the French Romantic sculptor Antoine-Louis Barye is in the central plaza. Originally created in 1832, the work is Barye´s allegory of the French Revolution of 1830, symbolizing the power of good (the lion) conquering evil (the serpent). This bronze cast was made about 1890. At the other end of the central plaza, within the reflecting pool, is Paul Manship´s Duck Girl of 1911, a lyrical bronze of a young girl carrying a duck under one arm – an early work by the same sculptor who designed the Aero Memorial for Logan Square. A favorite of the children is Albert Laessle´s Billy, a two-foot-high bronze billy goat in a small plaza halfway down the southwest walk. Billy´s head, horns, and spine have been worn to a shiny gold color by countless small admirers. In a similar plaza in the northeast walkway stands the Evelyn Taylor Price Memorial Sundial, a sculpture of two cheerful, naked children who hold aloft a sundial in the form of a giant sunflower head. Created by Philadelphia artist Beatrice Fenton, the sundial memorializes a woman who served as the president of the Rittenhouse Square Improvement Association and Rittenhouse Square Flower Association. In the flower bed between the sundial and the central plaza is Cornelia Van A. Chapin´s Giant Frog, a large and sleek granite amphibian. Continuing the animal theme, two small stone dogs, added in 1988, perch on the balustrades at the southwest corner entrance. At Night Once predominantly a daytime destination, Rittenhouse Square is now a popular nightspot as well, with a string of restaurants – including Rouge, Devon, Parc and Barclay Prime – that have sprouted up along the east side of the park on 18th Street. So these days, you can take in the serenity of the natural landscape from a park bench in the sunshine and then sip cocktails under the stars at one of many candlelit outdoor tables. Meanwhile, several more restaurants, bars and clubs have opened along the surrounding blocks in recent years, like Parc, Tria, Continental Midtown, Alfa, Walnut Room, and Twenty Manning just to name a few.
The Experience The Liberty Bell has a new home, and it is as powerful and dramatic as the Bell itself. Throughout the expansive, light-filled Center, larger-than-life historic documents and graphic images explore the facts and the myths surrounding the Bell. X-rays give an insider´s view, literally, of the Bell´s crack and inner-workings. In quiet alcoves, a short History Channel film, available in English and eight other languages, traces how abolitionists, suffragists and other groups adopted the Bell as its symbol of freedom. Other exhibits show how the Bell´s image was used on everything from ice cream molds to wind chimes. Keep your camera handy. Soaring glass walls offer dramatic and powerful views of both the Liberty Bell and Independence Hall, just a few steps away. History The bell now called the Liberty Bell was cast in the Whitechapel Foundry in the East End of London and sent to the building currently known as Independence Hall, then the Pennsylvania State House, in 1753. It was an impressive looking object, 12 feet in circumference around the lip with a 44-pound clapper. Inscribed at the top was part of a Biblical verse from Leviticus, "Proclaim Liberty throughout all the Land unto all the Inhabitants thereof." Unfortunately, the clapper cracked the bell on its first use. A couple of local artisans, John Pass and John Stow, recast the bell twice, once adding more copper to make it less brittle and then adding silver to sweeten its tone. No one was quite satisfied, but it was put in the tower of the State House anyway. Fast Facts The Liberty Bell is composed of approximately 70 percent copper, 25 percent tin and traces of lead, zinc, arsenic, gold and silver. The Bell is suspended from what is believed to be its original yoke, made of American elm. The Liberty Bell weighs 2,080 pounds. The yoke weighs about 100 pounds.
The Experience Museum Without Walls: AUDIO is a multi-platform, interactive audio tour, designed to allow locals and visitors alike to experience Philadelphia extensive collection of public art and outdoor sculpture along the Benjamin Franklin Parkway and Kelly Drive. This innovative program invites passersby to stop, look, listen and see this city public art in a new way. Discover the untold histories of the 51 outdoor sculptures at 35 stops through these professionally produced three-minute interpretive audio segments. The many narratives have been spoken by more than 100 individuals, all with personal connections to the pieces of art. Works in Museum Without Walls: AUDIO include the sculpture Jesus Breaking Bread, which is located in front of the Cathedral Basilica of Saints Peter and Paul at 18th and Race Streets. The sculpture´s audio program features the voices of three people who are each intimately, yet distinctly, connected to the piece. Listeners can hear Martha Erlebacher, the wife of the now-deceased sculptor and an artist herself, recall the personal challenge Walter Erlebacher set to humanize the figure. Monsignor John Miller, who oversaw the commission of the sculpture for the Archdiocese of Philadelphia, discusses the artist confrontation with historic interpretation, and Sister Mary Scullion, who runs the renowned program for the homeless in Philadelphia, Project H.O.M.E., and who also attended the sculpture dedication as a student, talks about the importance of placing the figure outside of the church. In the audio program for the sculpture Iroquois, listeners will hear a first-person account from Mark di Suvero, the artist himself, who discusses the abstract sculpture and its open shapes that invite public interaction and viewing from multiple angles. I think that in order to experience [Iroquois] … you have to walk in through the piece, you have to have it all the way around you and at that moment, you can feel what that sculpture can do, says di Suvero. Lowell McKegney, di Suvero construction manager and longtime friend, compares the sculpture to music and encourages listeners to appreciate it in the same way. History Philadelphia has more outdoor sculpture than any other American city, yet this extensive collection often goes unnoticed. This program is intended to reveal the distinct stories behind each of these works, that have become visual white noise for so many of the city residents and visitors.


text:
TRANSPARENCY: A cornerstone value of the Governor
by Office of the Governor | Mar 11, 2014 | Press Releases
The Governor has just come under another verbal attack from the acting speaker. This time, the allegation is that the Governor is not transparent. These allegations were made in the acting speaker's weekly radio address. We do not wish to engage in any back and forth dispute, especially during this holy season. The only thing we will present here is a defense of the Governor, backed up by facts.
The acting speaker's claims are baseless, have no merit, and are not backed up by any facts. Transparency is a cornerstone value of the Calvo Tenorio administration; any attempt by politicians to lie about this record will be met with a quick dose of the truth. This, of course, always will be backed by fact, data, and credible information.
While there is much we can say and show to defend the Governor's record on transparency, here is what the experts on financial transparency have to say about Governor Calvo and his administration:
Standard & Poors
Guam, the U.S. territory 4,000 miles (6,400 kilometers) west of Hawaii, had its rating raised to BB-from B+ by Standard & Poor's on signs of a strengthening financial position.
"The rating action reflects our view of the government's improved financial management practices, including improved transparency, stricter fiscal discipline and enhanced cash flow monitoring procedures and capabilities," Paul Dyson, a San Francisco-based S&P analyst, said today in a report.
Government Finance Officers Association
The Government Finance Officers Association awarded the Certificate of Achievement for Excellence in Financial Reporting to GovGuam. The Certificate of Achievement is the highest form of recognition for government accounting and financial reporting. This honor was awarded to DOA for preparing the Comprehensive Annual Financial Report for fiscal year 2012. Every governor has been mandated by the Organic Act since 1950 to submit a CAFR every year. GovGuam met this federal mandate for the first time in 63 years in 2013 under the leadership of Gov. Calvo.
According to the GFOA, the "CAFR has been judged by an impartial panel to meet the high standards of the programincluding demonstrating a constructive 'spirit of full disclosure' to clearly communicate its financial story and motivate potential users and user groups to read the CAFR."
The CAFR prepared by DOA disclosed the government's finances for Fiscal Year 2012. The report includes audited financials, including balance sheets, statements of revenues and expenditures, statements of cash receipts and disbursements, transfers in and out from accounts, etc. This is the information senators need to make informed policy decisions that consider the government's financial condition. It also is a useful report for the public to use to judge the administration's management practices using real data.
Puerto Rico and Guam, two U.S. territories whose debt is tax-exempt nationwide, are navigating uncharted waters.
The island's CAFR earned it a "Certificate of Achievement for Excellence in Financial Reporting" from the Government Finance Officers Association, said Jeffrey Esser, the group's executive director in Chicago. It was the only territory to get the award for 2012 reporting, he said in an interview. Puerto Rico last received the distinction in 2007.
"It shows increased professionalism in a case like Guam," Esser said. "It shows that the financial information they produced is high-quality, and it can be relied on. It's really hard work, especially for the first time."
Indeed, in the latest report to the Attorney General on the administration's compliance with the Freedom of Information Act, all but three FOIA requests were granted with responses. The three that went without response were given reasons as defined in 5 GCA §10108. If Sen. Respicio has an issue with that, then perhaps he, as a lawmaker, should revisit that law.
Other examples of unprecedented efforts toward transparency:
– January 2011 disclosure of the cash- and financial-position of the government of Guam to the public via the media. This eventually led to the Legislature bowing to public demand for their cooperation on the Governor's fiscal policies.
– These fiscal policies included the eventual payment of tax refunds via debt refinancing, where the debt burden was moved from the people to the bank. This happened despite Sen. Rory Respicio insisting that he'd rather "owe the people than the bank." Click here to view this statement from the Senator.
– February 6, 2011 directive from the Governor's COS to all employees removing all existing gag orders at the time, reinforcing employees' rights to speak to the media, directing the free flow of public information, etc.
– Directive from the Governor to the police department to reopen the Blue House case and to report findings as quickly as possible to the public.
– Unprecedented, near-on-demand access reporters have to the Governor on any issue they wish to speak with him about.
– Unprecedented releases of information on the operations, projects, programs, and goings-on of your government. This ranges from:
o Several news releases daily
o Three weekly columns in the island's newspapers from the Governor, the Lieutenant Governor, and the Islandwide Beautification Task Force
o Two weekly and one biweekly talk show appearance by the Lieutenant Governor, his wife, or the IBTF on their efforts
o One weekly broadcast address to the people from the Governor
o One weekly segment by the Governor's Communications Office on NewsTalk K57's The Big Show with Travis Coffman on a range of topics in the government
o A Customer Service Hotline dedicated to taking residents' complaints and suggestions, then fixing the problems
o A weekly newsletter
o A 24-hour channel
o On-demand access to the Governor's senior staff and Cabinet to talk radio and journalist questions
o Constant engagement on Facebook, Twitter, Instagram, email, and phone
Finally, it should be noted that Governor Calvo, in his last year as a senator, introduced legislation that would have cut the number of days the government had to respond to requests for information under the Freedom of Information Act. The legislative majority did not allow the bill to be placed on session agenda, and never again took up the measure.
It should also be noted that the person making these accusations against Gov. Calvo is the same person who adjusted pay for senators in December 2010 and told no one until the media uncovered the truth months later. This senator, along with some of his colleagues, have refused to roll back the pay raise each and every time they are confronted with this question.
The additional allegation from the acting speaker that whistleblowers are retaliated against also is baseless. There is not a single instance we are aware of. We have constantly encouraged employees to speak up about any wrong doing that has occurred. Employees have spoken up several times, leading to better service and the correction of misunderstandings.
Transparency, though it can always be better, is more alive and healthy today than it has ever been. It is not merely a buzzword for Governor Calvo. It is not something he measures by the letter of the law. This is a value he holds in every action he takes and every decision he makes.
This should be called what it transparently is: the latest in a political attack against the Governor. Transparently, it is done in an election year from a politician, who covets the power of the office, and not the duty the office possesses to serve the people.
We welcome any effort by sincere people to improve transparency and access to the people's government. But we will not waste any more time entertaining another needless assault on the character of the administration from a politician slinging mud… especially when the facts speak for themselves.


Vietnam Wall Guy, The - GI Film Festival | Reel Stories! Real Heroes!
A conversation with Jan C. Scruggs on what it took to create the Vietnam Veteran Memorial Wall, and his efforts to fund the creation of the proposed Education Center to be built near the wall. The Vietnam Veteran Memorial Wall has become the most visited attraction in Washington, D.C.
With a career spanning over 25 years in Film, Television, and video production in Los Angeles, Matt has shifted to documentary producing and directing. Over the past 7 years he has produced and directed four feature length documentaries (two receiving Academy Award nominations) profiling our country's efforts to locate, recover, and repatriate the remains of those who gave their lives in WW II in the South Pacific. Matt continues to focus on subjects related to the military. His latest, a short subject on the "Stars N Stripes", newspaper to our military since the Civil War. His current entry in the GI Film Festival is a short documentary on Jan C. Scruggs, the force behind the most heavily visited tourist attraction in the nation, The Vietnam Veteran Wall, and on Jan's tireless efforts to fund an Education Center, near the Wall, to honor our military's sacrifice in defending our freedom since the founding of our country..


text:
Back to General Health
Comment: Amazing the real thing might work better than the synthetic. Dr. Eisenstein always suggested vitamin D as the first corner stone of health, but it was always D3! Synthetics always carry a greater risk for side effects due to their chemical structure.
Ergocalciferol has similar, if not better, efficacy and safety compared with calcitriol in treating nondialysis chronic kidney disease patients with mineral and bone disorder (CKD-MBD), a new study suggests.
Zhang Dongliang, MD, of Peking University International Hospital in China, and colleagues directly compared oral preparations of natural vitamin D2 with active vitamin D3 sterol in a randomized trial of 204 patients with CKD stages 3 to 5 not on renal replacement therapy. The dosing strategy for ergocalciferol was 50,000 units once weekly for the first 3 months, then 50,000 units once monthly, toward a target blood level of 25-hydroxyvitamin D [25(OH)D] of 30 ng/mL. Patients in the calcitriol group received a dose of 0.25 µg once daily to start that was later adjusted in response to 25(OH)D, calcium, phosphorus, and intact parathyroid hormone (iPTH).
Results showed that the 25(OH)D level in the ergocalciferol group increased significantly from 15.14 to 37.32 ng/mL over 33 months. It also increased more than in the calcitriol group, whose level rose from 14.90 to 18.08 ng/mL. The investigators observed no statistically significant difference between the 2 treatments in controlling calcium, phosphorus, and iPTH. Subgroup analyses by CKD stage also revealed no distinction in achievement of target iPTH. Only a small proportion of patients maintained target levels of all 3 markers, according to the researchers: 21.3% of ergocalciferol users and 20% of calcitriol users.
In line with previous research, ergocalciferol demonstrated safety. The 2 groups had similar rates of all-cause death, acute myocardial infarction, stroke, and congestive heart failure. Renal outcomes were also similar, including renal replacement therapy initiation, more than 25% decline in estimated glomerular filtration rate, doubling of serum creatinine levels, and hospitalization.
Since ergocalciferol treatment increased 25(OH)D levels and appeared to have other beneficial effects (decreasing alkaline phosphatase, cholesterol, and triglycerides, and stabilizing uric acid), "using nutritional vitamin D supplements like ergocalciferol in CKD patients with 25(OH)D insufficiency is recommended," Dr Dongliang and colleagues concluded in the European Journal of Pharmacology. The level of vitamin D considered sufficient in nondialysis CKD-MBD patients is controversial, so optimal dosing and frequency of vitamin D remains uncertain.
Source1. Dongliang Z, He L, Daoxin Y, LiYan W, Yao M. Ergocalciferol Versus Calcitriol for Controlling Chronic Kidney Disease Mineral Bone Disorder in stage 3 to 5 CKD: a Randomized Controlled Trial. Eur J Pharmacol. 2016 Jul 8. pii: S0014-2999(16)30449-6. doi: 10.1016/j.ejphar.2016.07.019.


The San Francisco 49ers fell to 1-4 on Sunday after a 28-18 defeat at the hands of the Arizona Cardinals. A fumble returned for a touchdown late in the fourth quarter sealed Arizona's win. Here's what we learned in Week 5.
1. The 49ers had the ball, trailing by just two points, before Haason Reddick had a strip sack of C.J. Beathard. Josh Bynes scooped up the loose ball and returned it 23 yards to the house. San Francisco had five turnovers - three lost fumbles and two interceptions. Conversely, the 49ers defense wasn't able to get any takeaways.
2. Beathard threw for 349 yards, two touchdowns and two picks. He also added a 1-yard touchdown run. San Francisco opened the game with an 8-play, 75-yard touchdown drive that was capped by a 5-yard shovel pass to Matt Breida. Beathard's second touchdown came on 4th-and-goal from the 1-yard line. Beathard rolled to his right and found Taylor at the front pylon. That score pulled the 49ers to within two points, however, the ensuing two-point conversion attempt was no good. It felt like a step backward for Beathard and the offense as the group was fairly stagnant for most of the game.
3. San Francisco's defense was pretty darn good apart from one play. Josh Rosen hit Christian Kirk for a 75-yard touchdown on Arizona's first play from scrimmage. From there, the 49ers limited the Cardinals offense. Rosen threw for just 170 yards on 10-of-25 passing, but he didn't turn the ball over. San Francisco held David Johnson to just 55 yards on 18 carries. Johnson did score twice, though, once in the second quarter and again late in the fourth quarter once the game was already decided. Larry Fitzgerald had just 35 yards on two receptions. Arizona finished the game with just 10 first downs and just 2-of-12 on third down.
4. Kyle Juszczyk and George Kittle paced San Francisco's pass catchers. Kittle had 83 yards and continues to be the 49ers most dangerous target in the passing game. Juszczyk added six receptions for 75 yards. The fullback has turned into San Francisco's third-down running back. The 49ers wide receivers were quiet again in this one. Trent Taylor posted seven receptions for 61 yards and a score. Pierre Garçon had five receptions for 47 yards on 12 targets.
5. The 49ers lost Breida to an ankle injury in the first half, and he did not return. He was cooking before getting hurt, racking 56 yards on just eight carries. He posted a pair of 17-yard runs. Alfred Morris assumed most of the workload with Raheem Mostert pitching in.
6. It wasn't a banner day for the 49ers special teams. Robbie Gould's streak of 33 consecutive made field goals came to an end on Sunday. Gould missed a 45-yarder in the second half. The 49ers also aborted the point after try following the opening drive touchdown as Bradley Pinion couldn't get the hold down. It was a costly miscue because San Francisco was unable to convert a potential game-tying two-point conversion following Taylor's fourth quarter touchdown.


text:
I Thought I'd Seen Everything è una canzone rock scritta da Bryan Adams, Eliot Kennedy e Robert John "Mutt" Lange per il decimo album in studio di Adams 11 del 2008.

Il brano
Lo stile musicale del brano è dichiaratamente ispirato alla musica rock e pop degli anni ottanta. Il singolo è stato pubblicato come download digitale nel Regno Unito a gennaio e come CD nel resto del mondo a marzo.

Nel 1991 Robert Lange scrisse una canzone con lo stesso titolo per la sua ex moglie, Stevie Vann. Tuttavia, secondo il sito ufficiale di Adams, si tratta soltanto di una coincidenza dato che questa canzone e quella realizzata da Lange sono due componimenti distinti.

Il video
Il video prodotto per I Thought I'd Seen Everything è stato diretto da Bryan Adams, per la prima volta alla regia, dopo essersi lamentato della malriuscita di alcuni suoi vecchi videoclip, diretti da altri. Il video, reso disponibile sul sito di Bryan Adams, vede il cantante ed il suo gruppo cantare il brano live in uno studio di incisione, similarmente a quanto veniva mostrato nel video di Please Forgive Me del 1993. In una intervista rilasciata a Dominick A. Miserandino, Bryan Adams ha dichiarato di aver voluto mostrare nel video ciò che egli veramente è, senza troppi abbellimenti.

Tracce
CD Single
 I Thought I'd Seen Everything - 5:07
 Miss America - 3:57
 The Way of the World - 3:18

Digital Download
 I Thought I'd Seen Everything - 3:57

Classifiche

Note

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


text:
Gary McAllister
Man charged over assault on Leeds United legend Gary McAllister
Gary McAllister was taken to hospital for treatment after suffering injuries in the incident
Gary McAllister was assaulted on Call Lane in Leeds city centre (Image: (Image: Andrew Milligan/PA Wire))
A man from Leeds is set to make a court appearance this week after he was charged in connection with an alleged assault on Leeds United legend Gary McAllister.
The former Whites midfielder and manager was in Leeds city centre at around 4am on Sunday, March 24 2019 when he was involved in an altercation on Call Lane.
McAllister was taken to hospital for treatment to the injuries he sustained.
West Yorkshire Police have today confirmed that a man from Leeds has been charged by postal requisition with assault occasioning actual bodily harm.
Damien Swan, aged 33, of Greenmount Terrace, Beeston, is due to appear at Leeds Magistrates Court this Wednesday.
Download the LeedsLive app - You can download our free app for iPhone and iPad from the Apple App Store , or get the Android version from Google Play .
West Yorkshire Police
Leeds city centre


The Engage California Conference will equip pastors and lay leaders with the information, resources, and tools necessary to support and defend a Judeo-Christian worldview in the public square.
Hear from the leaders who have been leading the fight. They will equip and inspire you to join the growing movement of churches who are ready and willing to impact the culture for Christ.


Kaapeli-Light is a trademark of Suomi Type Foundry, Suomi Finland.
Estilo Pro Book is a trademark of Dino dos Santos _DSType.
RBNo2.1a BoldItalic is a trademark of Rene Bieder.
SF Diego Sans Outline Oblique is a trademark of the ShyFonts Type Foundry.
Oei is a trademark of David Kerkhoff & Stephanie Oei.
Copyright (c) 2010 by David Kerkhoff & Stephanie Oei. All rights reserved.
This font is free for personal use. Donation required for commercial use, like websites, blogs, print, corporate use, schools, etc. You can donate any amount you feel comfortable with through PayPal - hanoded@gmail.com , and mention 'Oei Font'. Should you have any questions regarding this license, don't hesitate to contact me. Future updates are free for people who have donated.
This font is free for personal use. Donation required for commercial use, like websites, blogs, print, corporate use, schools, etc. You can donate any amount you feel comfortable with through PayPal - hanoded@gmail.com Should you have any questions regarding this license, don't hesitate to contact me. Future updates are free for people who have donated.
Superglue is a trademark of Ray Larabie.
Otama Text Bold Italic is a trademark of Tim Donaldson.


text:
var assert = require( 'assert' );

module.exports = {
	description: 'correct statement order is preserved even in weird edge cases',
	context: {
		getAnswer: function ( obj ) {
			return obj.answer;
		}
	},
	exports: function ( exports ) {
		assert.equal( exports, 'right' );
	}
};

redpajama_set_name: RedPajamaGithub


text:
Illinois Matmen Q&A: University of Illinois redshirt senior Zane Richards
by Jared Bell January 18, 2017, 8:25 pm 8.6k Views 175 Votes
Photo Credit: Sam Janicki
By JARED BELL
Illinois Matmen
Zane Richards has one last run.
A two-time state champion at Carbondale High School, Richards is now a redshirt senior on this year's Illinois wrestling team and is one of the Fighting Illini's best wrestlers.
A 2016 All-American and a three-time NCAA Qualifier, Richards is currently 14-2 this season at 133 pounds and is looking to break through and win his first national championship.
Recently, Illinois Matmen caught up with Richards to discuss his national-title quest, the one thing most people don't know about him and life after college wrestling.
Illinois Matmen: Can you talk about the season and how it's gone so far?
Richards: It's been an interesting season so far. I started out doing well in a couple of tournaments before we went to the Midlands, where I took a loss. I also took a loss last week, but at all the other tournaments and duals I've been able to win.
I'm definitely learning every step of the way, and everything is gearing toward the Big Ten (Championships) and the National (Championships) later this season (in March). It's all a process, so I have to understand that, be focused and ready to go every day in the wrestling room.
Illinois Matmen: You're in your final collegiate season, so what's it like to know that you have one last chance at a national title?
Richards: It's a great opportunity and a moment that you have to seize, just like it's been every year since Year 1.
Every wrestler wants to qualify for the national tournament, and that definitely motivates me, but more so the focus is working on the things I need to do to get that title. I don't think being a senior necessarily motivates me alone.
Illinois Matmen: Who do you train with in the Illinois wrestling room?
Richards: I train with a lot of the guys around my weight, including a lot of the new freshmen in (Montini graduate Dylan) Duncan, (Prairie Ridge graduate Travis) Piotrowski and (St. Rita graduate Jake) Silzer. We also have the ROTC practices once in a while, so I wrestle (Illinois graduate and two-time national champion Jesse) Delgado in Freestyle. (Former NCAA champion and Illinois assistant coach) Jeremy Hunter is also still here and once or twice a week he'll get on the mat and roll around with us, so I have plenty of workout partners.
All of those guys have been great to train with and have really pushed me to become better.
Illinois Matmen: A lot of high school wrestlers have the dream of wrestling in college, so what advice would you give those kids looking to pursue that dream?
Richards: I would say make it your passion and make it your dream, and by making it your dream you're going to have to sacrifice things for that dream. It's very doable if it becomes your life, but also you have to enjoy it and know that you can do it.
And don't just set your dream of 'I want to be on a Division I team' or 'I want to be a starter.' Dream of being a national champ and understand what you have to do to get that done, and go for it. There's no reason why you shouldn't make an attempt. Prove to yourself that you can do great things. Even if it's difficult, it's always possible.
Illinois Matmen: What's one thing most people don't know about you? Do you have any hidden talents or interests?
Richards: Outside of wrestling, I really enjoy rock music a lot and just music in general. I listen to Tool or Chevelle and the Red Hot Chili Peppers. Really, I'm a 90s grungy guy and a 90s alternative guy, and even the harder stuff is pretty cool.
Illinois Matmen: When the season is done and you don't have to watch your weight, what's the one food you'll eat first?
Richards: Luckily, I haven't even thought about it because my weight is usually pretty good, so if I have something that I'm really craving I can eat it.
But if I had to pick something, it'd probably be a great big burrito or something like that.
Illinois Matmen: When you're done wrestling at Illinois, what do you hope people say about you and your career?
Richards: Honestly, people can say whatever they want to say about me and it's not something I think about a whole lot because I don't feel like I'm doing this for other people. I'm doing this for myself.
I guess if people do say something about me I hope that it's I gave 100-percent effort, left nothing and really went after it.
Illinois Matmen: What do you envision doing in life after college wrestling?
Richards: There is no life outside of wrestling (laughs).
In all seriousness, after college, I expect to train for the next level and compete internationally. Outside of that, I'd like to give back and coach. I'd like to stay in wrestling for as long as I can, even if that's part-time coaching as a minimum.
Jared Bell can be reached at (815) 220-6938. Follow him on Twitter @NT_SportsJared.
Previous article GO EARN IT Wrestling Apparel High School Rankings 1/17
Next article Wrestling community rallies behind Medlin family after destructive house fire
Written by Jared Bell
More From: College
B1G: 18 Former Illinois Wrestlers Qualify for the NCAA's
by Illinois Matmen March 8, 2022, 7:32 pm
Wrestler of the Week – Will Lewan
by Illinois Matmen February 12, 2022, 9:30 am
Wrestler of the Week – Dylan Duncan
by Illinois Matmen February 6, 2022, 3:58 pm
Previewing the Illinois Matmen Open
2021 SIUE Cougar Clash Preview
by Illinois Matmen December 2, 2021, 7:57 pm
Huskie Grapplers Ready for Red-Black Duals
by Illinois Matmen October 28, 2021, 12:24 am
GO EARN IT Wrestling Apparel High School Rankings 1/17
Wrestling community rallies behind Medlin family after destructive house fire


text:
Q: rails 3 customize validator error I am following Ryan Bates' Railscast. I find when I tried to establish my customized field validator, my rails 3 is not working as expected.
I established a new email_format_validator.rb file in under lib/ and the codes are:
class EmailFormatValidator < ActiveModel::EachValidator
  def validate_each(object, attribute, value)
    unless value =~ /^([^@\s]+)@((?:[-a-z0-9]+\.)+[a-z]{2,})$/i
      object.errors[attribute] << (options[:message] || "is not formatted properly")
    end
  end
end

I put this line in my user.rb (Model file):
validates :email, :presence => true, :uniqueness => true, :email_format=>true

The browser complained:
Unknown validator: 'email_format'
Why? How to solve this?

A: You will need to restart your server. The lib directory isn't loaded by default, so you'll need to restart your Rails server in order to load this validator.

Edit:
Try putting them under lib/validators and restarting the server...

A: I put 'email_format_validator.rb' under 'config/initializers'. And then restart the server. Everything is working now..

redpajama_set_name: RedPajamaStackExchange


On Friday the 26th January come and enjoy The JOHN HINSHELWOOD BAND.
£5.00 suggested donation. Cakes + coffee/tea.
It's just over a year since our last Bake Off which was a great success, so we decided to do it again. You do your baking at home, bring it in the morning and then everyone can come and sample the results. There will be various categories again e.g. sponges, loaves, pancakes, biscuits, preserves, children's section, men's section, under-fives. This year, we are going to have a 'Signature Challenge' where there will be a set recipe that everyone has to follow and we can all compare the results. We hope to have some judges from the local community again with various prizes for the best entries. This should be a fun event for all ages, even if you can't bake, come along and enjoy some of the entries with a tea, coffee or juice. Any proceeds that we make are going to support Cambuslang and Rutherglen Reachout Trust who work with local schools and churches to spread the news of Jesus amongst young people in our area. Look out for more information over the coming weeks, but in the meantime - "On your marks, get your recipes out BAKE!!!"
If you want to know more, please contact Jennifer Menzies on 647 4664 or menzies06@btinternet.
Pre-Hogmanay night featuring a variety of talented musicians. Proceeds from this special evening will go to the Salvation Army and Burnside in Bloom.
Andrew McTaggart and Caledonia Voices will be here in Stonelaw for their ever popular Christmas Concert on Monday 18th December at 7:30 pm. With beautiful music by Rutter and well known carols it promises to be another wonderful evening. Definitely an opportunity to invite your music loving friends along to Stonelaw. Tickets, priced £10, please pay at the door.
Come along and enjoy a short, informal time of worship @ the Meeting Place on the 3rd December at 6.30pm. The theme is 'Road less Travelled'.
Our invited guest is Peter Hagenbuch. Peter plays in a bluegrass band called Albakirkie who regularly play at festivals, clubs and churches.
Peter was born in Cambridge in 1954 and moved to Canterbury when he was 10. He started playing guitar when he was 12 and learned to fingerpick, playing songs by Ralph McTell, Al Stewart, Michael Chapman and others. In his 20s he started to play mandolin and flatpicking bluegrass guitar.
At university he got interested in pig breeding and went on to work on pig farms in Stoke Mandeville and Switzerland then with the Meat and Livestock Commission in Bletchley. Around this time, he became treasurer of Milton Keynes Guide Dogs. As the group were discussing fundraising ideas Peter remembered being inspired as a teenager, reading about a 50-mile walk in the Kentish Gazette, from Margate to London. He did his first 50-mile walk from London to Milton Keynes in 1982, raising £159 for Guide Dogs and a deaf charity – his sister has two deaf children. He got married in 1983 and in 1986 accepted a job with a chicken breeding company and moved to Uphall in West Lothian.
Peter and Wendy have two daughters. The oldest runs a cat sitting business called Team Feline. The second has cerebral palsy. Through her he has been involved with disability sport, especially the game of boccia, which is a Paralympic sport – Peter is a qualified referee.
He was brought up in the church but I stopped attending when he left school and home. Nearly twenty years later he returned to the church and came to faith at the age of 37, on Easter Day 1992.
In 2005 he went to Honduras for two weeks with the Christian charity Tearfund on their Transform Programme. The idea is that you spend time in a developing country and are transformed by the experience – it changes your outlook on life. After he returned from Honduras he started sponsoring a child from Honduras with the charity Compassion. Since then he has sponsored many other children. Peter currently sponsors 29 children.
His trip to Honduras was the start of a Latin American adventure which took him back to Honduras, then to the Dominican Republic, Uruguay and Brazil. He's also been to India and Kenya. All these trips were in connection with child sponsorship, charities and projects that he supports.
Peter continues to do 50-mile walks, nearly every year. This year will be his 29th 50-mile walk and has raised around £50,000 for various charities from these walks.
Stonelaw Church is joining with other Church of Scotland congregations in having a Prayer Day on Saturday 25th November 2017. The day will start with a prayer breakfast at 9am in the hall, continue all day in the church where there will be four prayer focus areas and conclude with a brief 7pm service. We're not expecting people to attend everything all day but we do hope you will join in as and when you can during the day.
We are sending written invitations to the whole Stonelaw church family so please pass the word on to groups you attend and extend a warm invitation to get involved. As the day is all about praying we are specifically asking for prayer requests. Where appropriate these will be displayed in one of the four prayer focus areas in the church. Please pass your prayer requests to myself, Alistair May or drop them in the prayer requests box at the front of the church. If you have any questions or comments about this event, then please do get in touch.
We are holding a Holiday Club style event for pre-school and primary age children on the afternoon of Saturday 9th December.
More details to follow, but in the meantime keep the date free and mention it to friends and family.
For more information or if you are willing to help, please speak to Jennifer Menzies 647 4664.
The National Mission Team is running a Coffee Morning on Saturday 7th October from 10:30 – 12:30. Tickets are priced £2.50 and £1.50 for under 16s. There will be a Home Baking Stall and again, we would welcome donations of baking from the congregation.
Thinking ahead to Christmas already?
Would a Christian Aid charity gift be perfect for a friend, or someone in your family?
To find out more about Christian Aid's work, you can go to www.christianaid.org.uk or call support worker Juliet in the Glasgow Office on 0141 221 7475.


text:
1421 Consulting Group Beijing
Beijing is much more than the capital city of China, a provincial-level administrative region, a municipality directly under the central government. Beijing is also the political center, cultural center, international communication center and scientific and technological innovation center of the PRC. Foreign enterprises have become an important force in Beijing's economic and social development. By the end of 2019, foreign enterprises were responsible for nearly 40% of the city's total industrial output, a quarter of total patents issued, and a third of its fiscal revenue.
As 1421's first China office and headquarters, the 1421 Consulting Group Beijing was established in 2011. 9 years of local presence and operations have equipped us with strong knowledge and networks to support our western clients. By being located in this policy pioneering city of Beijing, we have assisted our clients in many government related industries, such as healthcare and renewable energy, to set up their companies and develop their business in Beijing. The Beijing office actively supports 1421 Shenzhen and Chengdu office on consulting and corporate service projects throughout all of mainland China.
Chinese Liang Hui 2018: What are the opportunities for foreign enterprises?
Liang Hui (两会) is the Chinese name for the most important Chinese national conferences. It translates into "Two Sessions" in English. This year the 13th Chinese Two Sessions have been successfully...
How to Move Forward after Negotiating in China
Negotiating in China can be a challenging task. Chinese are strategists who see business as battle. Many Chinese businessmen and –women use the teachings of Sun Tzu for negotiating. In "The Art of...
How to Prepare Business Negotiations in China
It is important to prepare business negotiations in China. Chinese are strategists who see business as battle. Many Chinese businessmen and –women use the teachings of Sun Tzu for negotiating. In...
Takeaways from the Chinese Two Sessions 2020
During the second day of the Chinese Two Sessions 2020, Premier Li Keqiang delivered the government work report. This document highlights the progress of China and the Party over the 2019 year and...
Business Negotiations in China
Business negotiations in China can be a challenging task. Chinese are strategists who see business as battle. Many Chinese businessmen and –women use the teachings of Sun Tzu for negotiating. In...
Post-COVID-19 China: Thoughts From our Consultants
At the beginning of 2020 the COVID-19 pandemic started in China. The virus was first discovered in Wuhan at the end of December 2019. However, it had spread throughout China by the end of January...
Virtual Offices in Beijing can no longer be Registered Addresses
"The registered address you have applied has been registered by many companies already, which has caused safety issues. According to the government request, related government bureaus are going to...
Beijing Office Address:
Room A-B 509, No. H2 DIYANG Tower,
North Dongsanhuan Road, Chaoyang
District, Beijing, 100027, P.R. China
info@1421.consulting
Interested in doing business in Beijing? Send Maxime a message!


Covered by the Axminster 3 year Guarantee, these products are designed and intended to be used in the home for light work and not for continuous use. Must be maintained and serviced in line with our schedule. Guarantee is void when used for business or education purposes.
It's probably the most comprehensive free guarantee ever - look for the icon and put your trust in Axminster. So sure are we of the quality, we cover all parts and labour free of charge for three years.
The Axminster Craft AC1400B bandsaw is our smallest model and is designed to be bench mounted.
It features a new style welded steel chassis with a cast iron table for strength and stability as well as a solid rip fence which locks rigidly. It's a straightforward machine, with a direct drive motor and balanced cast alloy wheels. Blade width capacities range from 6-13mm; it also has copper blade guides and ball bearing thrust guides. These combine to effectively control the blade allowing thin slices of veneer to be cut and the top guide even has a rack and pinion height control. The top wheel is mounted in a welded steel sub frame with blade tensioning and tracking controls conveniently close. A single dust outlet port provides efficient dust removal when connected to a suitable vacuum extractor.
The machine is supplied with a 6mm 6tpi general purpose blade made from UK manufactured stock. A selection of different blades are available to suit many jobs.
This is a really effective little bandsaw and would be superb for the hobby or craft workshop or as an additional machine for smaller work.
This product is on page 20 of the Axminster Tools & Machinery 2018/19 Catalogue.


'Captain Marvel': Where Was Carol for 25 Years Before 'Avengers: Endgame'?
By placing it on the calendar less than two months ahead of "Avengers: Endgame," Marvel Studios was seemingly setting up the "Captain Marvel" movie to have some kind of significance in the greater story of the Marvel Cinematic Universe. Which, then inspired a lot of questions coming into the movie about how exactly it would contribute beyond just introducing Carol Danvers as a character.
But there are two questions that are most immediately pressing. Where the hell has she been? And if Nick Fury (Samuel L. Jackson) knew her back in the day and is able to call her for help, then why hasn't he brought her in already for one of the other world-shattering calamities our heroes have had to stop?
And yet after watching "Captain Marvel" we still don't know the answers to those questions — they'll have to come in "Avengers: Endgame" in April if they do at all. But just because we don't know that doesn't mean we can't make some guesses.
So at the end of "Captain Marvel," there are two relevant scenes. The first sees Carol return a pager to Fury that she took from him earlier in the movie, but with some modifications. Now, she says, he should be able to contact her if she's within "two or three galaxies" from Earth. She tells Fury he should use it for "emergencies only," though she doesn't specify what constitutes an emergency. And that's that.
And in the second, she uses her newly-unlocked powers — which it turns out she received from the Tesseract, AKA the Space infinity stone — to physically move the star cruiser that carrying Skrull refugees out of our solar system and toward an unknown location. And that is also that.
Carol's explanation for the pager does provide a potential reason why Fury didn't called her in to help when Loki (Tom Hiddleston) invaded New York with his Chitauri forces, or when Ultron tried to kill everyone on Earth — maybe he did try to use the pager but she was somewhere the pager couldn't reach.
That is somewhat more plausible than it may initially sound. The Kree Empire is actually based in the Large Magellanic Cloud rather than the Milky Way, and the Kree are clearly capable of traveling to other galaxies since they do so in "Captain Marvel." So in order to take the Skrull refugees someplace the Kree can't get to them, they would have to go beyond the Milky Way.
And maybe they even ended up traveling to a different plane of existence to find shelter, like the Quantum Realm. Despite the totally out there way it's depicted in the "Ant-Man" movies, the Quantum Realm is in fact home to entire civilizations — in the comics it's called the Microverse and it's more or less just another place in the universe. Though communication between our world and the Quantum Realm is clearly possible (as we see in "Ant-Man and the Wasp"), Fury's pager may not be equipped for that.
It's possible that Carol could travel to the Quantum Realm because her powers in the MCU came from the Tesseract. If any Infinity Stone could allow travel to the Quantum Realm it would be the one that can open wormholes to anywhere in the universe. And I previously speculated that the film version of Carol Danvers might obtain some of the powers of the quantum-powered superhero Quasar, who is able to tunnel from our universe to a place he calls the Quantum Zone as a sort of shortcut when he's traveling from planet to planet. That method of faster-than-light travel is not exclusive to Quasar in the comics — the Fantastic Four travels that way as well — and so the "lightspeed engine" thing that Mar-Vell was trying to use the Tesseract to create in 1989 could also work that way.
You can read plenty more about why I think Quasar's dimension-hopping abilities are relevant right here.
As for why Carol wouldn't have at least poked her head back in to check on Earth every once in a while, that would depend on what kind of adventures she got into while out wherever she took the Skrulls. We were vaguely expecting that the plot of "Captain Marvel" could tie into Thanos' backstory in some way — both because Mar-Vell and Thanos were arch-enemies in the comics and because you'd think there would be a reason for placing this movie where it is on the calendar — it's conceivable that Carol has some kind of run-in with Thanos while she's escorting the Skrulls around the universe. Thanos' Sanctuary is purposefully hidden in a remote corner of the cosmos, so Carol could try to hide the Skrulls there only to be met with a rude purple surprise.
If that's the case, then that bit of history would likely be explored in "Endgame." But that's really just a wild guess since "Captain Marvel" doesn't hint at anything like that. But given how crucial the Quantum Realm appears poised to be in "Endgame," Carol spending some time down there in this two-decade interlude seems like a distinct possibility.
It's easy to assume that this means Marvel had a specific reason for introducing her at that point in time. And, if you follow that thread, once they decided to set the movie in 1995 they would have come up with an explanation for where she's been this whole time. Here's hoping we'll get one come April.


The 11th international conference on Inductive Logic Programming, ILP2001, was held in Strasbourg, France, September 9-11, 2001. ILP2001 was co-located withthe3rdinternationalworkshoponLogic, Learning, andLanguage(LLL2001), and nearly co-located with the joint 12th European Conference on Machine Learning (ECML2001) and 5th European conference on Principles and Practice of Knowledge Discovery in Databases (PKDD2001). Continuing a series of international conferences devoted to Inductive Logic Programming and Relational Learning, ILP2001 is the central annual event for researchersinterestedinlearningstructuredknowledgefromstructuredexamples and background knowledge. One recent one major challenge for ILP has been to contribute to the ex- nentialemergenceofDataMining, andtoaddressthehandlingofmulti-relational databases. On the one hand, ILP has developed a body of theoretical results and algorithmicstrategiesforexploringrelationaldata, essentiallybutnotexclusively from a supervised learning viewpoint. These results are directly relevant to an e?cient exploration of multi-relational databases. Ontheotherhand, DataMiningmightrequirespeci?crelationalstrategiesto be developed, especially with regard to the scalability issue. The near-colocation of ILP2001 with ECML2001-PKDD2001 was an incentive to increase cro- fertilization between the ILP relational savoir-faire and the new problems and learning goals addressed and to be addressed in Data Mining. Thirty-seven papers were submitted to ILP, among which twenty-one were selected and appear in these proceedings. Several - non-disjoint - trends can be observed, along an admittedly subjective clustering. On the theoretical side, a new mode of inference is proposed by K. Inoue, analog to the open-ended mode of Bayesian reasoning (where the frontier - tween induction and abduction wanes). New learning re?nement operators are proposed by L. Badea, while R. Otero investigates negation-handling settings.


text:
Q: Xamarin for Visual Studio (2015) Breaking Bootcamp Windows 10 Sound and Wireless Drivers My computer is an iMac 5k (late 2015)
I have an issue where my bootcamp install of Windows 10 has nonworking audio drivers and wireless networking drivers after installing the default selection of cross platform mobile development pieces.
On my system this is 100% replicable.  All i have to do is create a bootcamp install of windows 10 64 bit.  Install visual studio keep defaults.  download and install the Xamarin for Visual Studio keep defaults.
After rebooting the sound driver has a red circle white x.  Wireless networking has a red circle white x.  Both drivers report all is well but neither work.  I have tried reinstalling the drivers from the apple drivers... I don't recall the name of the drivers installer.
I believe this is something do to with emulator hooks but i don't know where to begin.
Anyone have any thoughts?
As a side note once installed an uninstall doesn't correct the problem.  Whatever registry edits are made are not undone.

A: Hyper-V seemed to be the culprit.
After going to "Windows Features", unchecking Hyper-V and restarting the computer.  Both audio and wireless drivers are once again active and working.